Version: 1.1.1
Title: Confidence Intervals with Poisson Double Sampling
Description: Functions to create confidence intervals for ratios of Poisson rates under misclassification using double sampling. Implementations of the methods described in Kahle, D., P. Young, B. Greer, and D. Young (2016). "Confidence Intervals for the Ratio of Two Poisson Rates Under One-Way Differential Misclassification Using Double Sampling." Computational Statistics & Data Analysis, 95:122–132.
URL: https://github.com/dkahle/poisDoubleSamp
BugReports: https://github.com/dkahle/poisDoubleSamp/issues
LinkingTo: Rcpp
Imports: Rcpp, stats
License: MIT + file LICENSE
RoxygenNote: 7.1.2
Encoding: UTF-8
NeedsCompilation: yes
Packaged: 2022-05-09 23:07:48 UTC; david_kahle
Author: David Kahle ORCID iD [aut, cre], Phil Young [aut], Dean Young [aut]
Maintainer: David Kahle <david@kahle.io>
Repository: CRAN
Date/Publication: 2022-05-10 13:10:05 UTC

Compute the marginal MLE of phi

Description

Compute the marginal MLE of the ratio of two Poisson rates in a two-sample Poisson rate problem with misclassified data given fallible and infallible datasets.

Usage

approxMargMLE(
  data,
  N1,
  N2,
  N01,
  N02,
  l = 0,
  u = 1000,
  out = c("par", "all"),
  tol = 1e-10
)

Arguments

data

the vector of counts of the fallible data (z11, z12, z21, z22) followed by the infallible data (m011, m012, m021, m022, y01, y02)

N1

the opportunity size of group 1 for the fallible data

N2

the opportunity size of group 2 for the fallible data

N01

the opportunity size of group 1 for the infallible data

N02

the opportunity size of group 2 for the infallible data

l

the lower end of the range of possible phi's (for optim)

u

the upper end of the range of possible phi's (for optim)

out

"par" or "all" (for the output of optim)

tol

tolerance parameter for the rmle EM algorithm

Value

a named vector containing the marginal mle of phi

References

Kahle, D., P. Young, B. Greer, and D. Young (2016). "Confidence Intervals for the Ratio of Two Poisson Rates Under One-Way Differential Misclassification Using Double Sampling." Computational Statistics & Data Analysis, 95:122–132.

Examples


# small example
z11 <- 34; z12 <- 35; N1 <- 10;
z21 <- 22; z22 <- 31; N2 <- 10;
m011 <- 9; m012 <- 1; y01 <- 3; N01 <- 3;
m021 <- 8; m022 <- 8; y02 <- 2; N02 <- 3;
data <- c(z11, z12, z21, z22, m011, m012, m021, m022, y01, y02)

fullMLE(data, N1, N2, N01, N02)
margMLE(data, N1, N2, N01, N02)
approxMargMLE(data, N1, N2, N01, N02)


## Not run: 

# big example :
z11 <- 477; z12 <- 1025; N1 <- 16186;
z21 <- 255; z22 <- 1450; N2 <- 18811;
m011 <- 38;  m012 <- 90; y01 <- 15; N01 <- 1500;
m021 <- 41; m022 <- 200; y02 <-  9; N02 <- 2500;
data <- c(z11, z12, z21, z22, m011, m012, m021, m022, y01, y02)

fullMLE(data, N1, N2, N01, N02)
margMLE(data, N1, N2, N01, N02) # ~1 min
approxMargMLE(data, N1, N2, N01, N02)




## End(Not run)

Compute the profile MLE CI of phi

Description

Compute the profile MLE confidence interval of the ratio of two Poisson rates in a two-sample Poisson rate problem with misclassified data given fallible and infallible datasets. This uses a C++ implemention of the EM algorithm.

Usage

approxMargMLECI(
  data,
  N1,
  N2,
  N01,
  N02,
  conf.level = 0.95,
  l = 0.001,
  u = 1000,
  tol = 1e-10
)

Arguments

data

the vector of counts of the fallible data (z11, z12, z21, z22) followed by the infallible data (m011, m012, m021, m022, y01, y02)

N1

the opportunity size of group 1 for the fallible data

N2

the opportunity size of group 2 for the fallible data

N01

the opportunity size of group 1 for the infallible data

N02

the opportunity size of group 2 for the infallible data

conf.level

confidence level of the interval

l

the lower end of the range of possible phi's (for optim)

u

the upper end of the range of possible phi's (for optim)

tol

tolerance used in the EM algorithm to declare convergence

Value

a named vector containing the marginal mle of phi

References

Kahle, D., P. Young, B. Greer, and D. Young (2016). "Confidence Intervals for the Ratio of Two Poisson Rates Under One-Way Differential Misclassification Using Double Sampling." Computational Statistics & Data Analysis, 95:122–132.

Examples


# small example
z11 <- 34; z12 <- 35; N1 <- 10;
z21 <- 22; z22 <- 31; N2 <- 10;
m011 <- 9; m012 <- 1; y01 <- 3; N01 <- 3;
m021 <- 8; m022 <- 8; y02 <- 2; N02 <- 3;
data <- c(z11, z12, z21, z22, m011, m012, m021, m022, y01, y02)

waldCI(data, N1, N2, N01, N02)
margMLECI(data, N1, N2, N01, N02)
profMLECI(data, N1, N2, N01, N02)
approxMargMLECI(data, N1, N2, N01, N02)

## Not run: 

# big example :
z11 <- 477; z12 <- 1025; N1 <- 16186;
z21 <- 255; z22 <- 1450; N2 <- 18811;
m011 <- 38;  m012 <- 90; y01 <- 15; N01 <- 1500;
m021 <- 41; m022 <- 200; y02 <-  9; N02 <- 2500;
data <- c(z11, z12, z21, z22, m011, m012, m021, m022, y01, y02)

waldCI(data, N1, N2, N01, N02)
margMLECI(data, N1, N2, N01, N02)
profMLECI(data, N1, N2, N01, N02)
approxMargMLECI(data, N1, N2, N01, N02)




## End(Not run)

Compute the full MLEs

Description

Compute the MLEs of a two-sample Poisson rate problem with misclassified data given fallible and infallible datasets.

Usage

fullMLE(data, N1, N2, N01, N02)

Arguments

data

the vector of counts of the fallible data (z11, z12, z21, z22) followed by the infallible data (m011, m012, m021, m022, y01, y02)

N1

the opportunity size of group 1 for the fallible data

N2

the opportunity size of group 2 for the fallible data

N01

the opportunity size of group 1 for the infallible data

N02

the opportunity size of group 2 for the infallible data

Details

These are the closed-form expressions for the MLEs.

Value

a named vector containing the mles of each of the parameters (phi, la12, la21, la22, th1, and th2)

References

Kahle, D., P. Young, B. Greer, and D. Young (2016). "Confidence Intervals for the Ratio of Two Poisson Rates Under One-Way Differential Misclassification Using Double Sampling." Computational Statistics & Data Analysis, 95:122–132.

Examples


# small example
z11 <- 34; z12 <- 35; N1 <- 10;
z21 <- 22; z22 <- 31; N2 <- 10;
m011 <- 9; m012 <- 1; y01 <- 3; N01 <- 3;
m021 <- 8; m022 <- 8; y02 <- 2; N02 <- 3;
data <- c(z11, z12, z21, z22, m011, m012, m021, m022, y01, y02)

fullMLE(data, N1, N2, N01, N02)


## Not run: 

# big example :
z11 <- 477; z12 <- 1025; N1 <- 16186;
z21 <- 255; z22 <- 1450; N2 <- 18811;
m011 <- 38;  m012 <- 90; y01 <- 15; N01 <- 1500;
m021 <- 41; m022 <- 200; y02 <-  9; N02 <- 2500;
data <- c(z11, z12, z21, z22, m011, m012, m021, m022, y01, y02)

fullMLE(data, N1, N2, N01, N02)



## End(Not run)

Compute the marginal MLE of phi

Description

Compute the marginal MLE of the ratio of two Poisson rates in a two-sample Poisson rate problem with misclassified data given fallible and infallible datasets.

Usage

margMLE(data, N1, N2, N01, N02, l = 0.001, u = 1000, out = c("par", "all"))

Arguments

data

the vector of counts of the fallible data (z11, z12, z21, z22) followed by the infallible data (m011, m012, m021, m022, y01, y02)

N1

the opportunity size of group 1 for the fallible data

N2

the opportunity size of group 2 for the fallible data

N01

the opportunity size of group 1 for the infallible data

N02

the opportunity size of group 2 for the infallible data

l

the lower end of the range of possible phi's (for optim)

u

the upper end of the range of possible phi's (for optim)

out

"par" or "all" (for the output of optim)

Value

a named vector containing the marginal mle of phi

References

Kahle, D., P. Young, B. Greer, and D. Young (2016). "Confidence Intervals for the Ratio of Two Poisson Rates Under One-Way Differential Misclassification Using Double Sampling." Computational Statistics & Data Analysis, 95:122–132.

Examples


# small example
z11 <- 34; z12 <- 35; N1 <- 10;
z21 <- 22; z22 <- 31; N2 <- 10;
m011 <- 9; m012 <- 1; y01 <- 3; N01 <- 3;
m021 <- 8; m022 <- 8; y02 <- 2; N02 <- 3;
data <- c(z11, z12, z21, z22, m011, m012, m021, m022, y01, y02)

fullMLE(data, N1, N2, N01, N02)
margMLE(data, N1, N2, N01, N02)


## Not run: 

# big example :
z11 <- 477; z12 <- 1025; N1 <- 16186;
z21 <- 255; z22 <- 1450; N2 <- 18811;
m011 <- 38;  m012 <- 90; y01 <- 15; N01 <- 1500;
m021 <- 41; m022 <- 200; y02 <-  9; N02 <- 2500;
data <- c(z11, z12, z21, z22, m011, m012, m021, m022, y01, y02)

fullMLE(data, N1, N2, N01, N02)
margMLE(data, N1, N2, N01, N02)





## End(Not run)

Compute the marginal MLE confidence interval for the phi

Description

Compute the marginal MLE confidence interval of the ratio of two Poisson rates in a two-sample Poisson rate problem with misclassified data given fallible and infallible datasets.

Usage

margMLECI(data, N1, N2, N01, N02, conf.level = 0.95, l = 1e-10, u = 1e+10)

Arguments

data

the vector of counts of the fallible data (z11, z12, z21, z22) followed by the infallible data (m011, m012, m021, m022, y01, y02)

N1

the opportunity size of group 1 for the fallible data

N2

the opportunity size of group 2 for the fallible data

N01

the opportunity size of group 1 for the infallible data

N02

the opportunity size of group 2 for the infallible data

conf.level

confidence level of the interval

l

the lower end of the range of possible phi's (for optim)

u

the upper end of the range of possible phi's (for optim)

Value

a named vector containing the lower and upper bounds of the confidence interval

References

Kahle, D., P. Young, B. Greer, and D. Young (2016). "Confidence Intervals for the Ratio of Two Poisson Rates Under One-Way Differential Misclassification Using Double Sampling." Computational Statistics & Data Analysis, 95:122–132.

Examples


# small example
z11 <- 34; z12 <- 35; N1 <- 10;
z21 <- 22; z22 <- 31; N2 <- 10;
m011 <- 9; m012 <- 1; y01 <- 3; N01 <- 3;
m021 <- 8; m022 <- 8; y02 <- 2; N02 <- 3;
data <- c(z11, z12, z21, z22, m011, m012, m021, m022, y01, y02)

waldCI(data, N1, N2, N01, N02)
margMLECI(data, N1, N2, N01, N02)
profMLECI(data, N1, N2, N01, N02)
approxMargMLECI(data, N1, N2, N01, N02)

## Not run: 

# big example :
z11 <- 477; z12 <- 1025; N1 <- 16186;
z21 <- 255; z22 <- 1450; N2 <- 18811;
m011 <- 38;  m012 <- 90; y01 <- 15; N01 <- 1500;
m021 <- 41; m022 <- 200; y02 <-  9; N02 <- 2500;
data <- c(z11, z12, z21, z22, m011, m012, m021, m022, y01, y02)

waldCI(data, N1, N2, N01, N02)
margMLECI(data, N1, N2, N01, N02)
profMLECI(data, N1, N2, N01, N02)
approxMargMLECI(data, N1, N2, N01, N02)




## End(Not run)

poisDoubleSamp : Confidence intervals with Poisson double sampling

Description

Functions to create confidence intervals for ratios of Poisson rates under misclassification using double sampling. Implementations of the methods described in Kahle, D., P. Young, B. Greer, and D. Young (2016). "Confidence Intervals for the Ratio of Two Poisson Rates Under One-Way Differential Misclassification Using Double Sampling." Computational Statistics & Data Analysis, 95:122–132.

Compute the profile MLE CI of phi

Description

Compute the profile MLE confidence interval of the ratio of two Poisson rates in a two-sample Poisson rate problem with misclassified data given fallible and infallible datasets. This uses a C++ implemention of the EM algorithm.

Usage

profMLECI(
  data,
  N1,
  N2,
  N01,
  N02,
  conf.level = 0.95,
  l = 0.001,
  u = 1000,
  tol = 1e-10
)

Arguments

data

the vector of counts of the fallible data (z11, z12, z21, z22) followed by the infallible data (m011, m012, m021, m022, y01, y02)

N1

the opportunity size of group 1 for the fallible data

N2

the opportunity size of group 2 for the fallible data

N01

the opportunity size of group 1 for the infallible data

N02

the opportunity size of group 2 for the infallible data

conf.level

confidence level of the interval

l

the lower end of the range of possible phi's (for optim)

u

the upper end of the range of possible phi's (for optim)

tol

tolerance used in the EM algorithm to declare convergence

Value

a named vector containing the marginal mle of phi

References

Kahle, D., P. Young, B. Greer, and D. Young (2016). "Confidence Intervals for the Ratio of Two Poisson Rates Under One-Way Differential Misclassification Using Double Sampling." Computational Statistics & Data Analysis, 95:122–132.

Examples


# small example
z11 <- 34; z12 <- 35; N1 <- 10;
z21 <- 22; z22 <- 31; N2 <- 10;
m011 <- 9; m012 <- 1; y01 <- 3; N01 <- 3;
m021 <- 8; m022 <- 8; y02 <- 2; N02 <- 3;
data <- c(z11, z12, z21, z22, m011, m012, m021, m022, y01, y02)

waldCI(data, N1, N2, N01, N02)
margMLECI(data, N1, N2, N01, N02)
profMLECI(data, N1, N2, N01, N02)
approxMargMLECI(data, N1, N2, N01, N02)


## Not run: 

# big example :
z11 <- 477; z12 <- 1025; N1 <- 16186;
z21 <- 255; z22 <- 1450; N2 <- 18811;
m011 <- 38;  m012 <- 90; y01 <- 15; N01 <- 1500;
m021 <- 41; m022 <- 200; y02 <-  9; N02 <- 2500;
data <- c(z11, z12, z21, z22, m011, m012, m021, m022, y01, y02)

waldCI(data, N1, N2, N01, N02)
margMLECI(data, N1, N2, N01, N02)
profMLECI(data, N1, N2, N01, N02)
approxMargMLECI(data, N1, N2, N01, N02)



## End(Not run)

Compute the Wald confidence interval

Description

Compute the Wald confidence interval of a two-sample Poisson rate with misclassified data given fallible and infallible datasets.

Usage

waldCI(data, N1, N2, N01, N02, conf.level = 0.95)

Arguments

data

the vector of counts of the fallible data (z11, z12, z21, z22) followed by the infallible data (m011, m012, m021, m022, y01, y02)

N1

the opportunity size of group 1 for the fallible data

N2

the opportunity size of group 2 for the fallible data

N01

the opportunity size of group 1 for the infallible data

N02

the opportunity size of group 2 for the infallible data

conf.level

confidence level of the interval

Value

a named vector containing the lower and upper bounds of the confidence interval

Examples


# small example
z11 <- 34; z12 <- 35; N1 <- 10; 
z21 <- 22; z22 <- 31; N2 <- 10;
m011 <- 9; m012 <- 1; y01 <- 3; N01 <- 3;
m021 <- 8; m022 <- 8; y02 <- 2; N02 <- 3;
data <- c(z11, z12, z21, z22, m011, m012, m021, m022, y01, y02)

waldCI(data, N1, N2, N01, N02) 
margMLECI(data, N1, N2, N01, N02)
profMLECI(data, N1, N2, N01, N02)
approxMargMLECI(data, N1, N2, N01, N02)

## Not run: 

# big example :
z11 <- 477; z12 <- 1025; N1 <- 16186;
z21 <- 255; z22 <- 1450; N2 <- 18811;
m011 <- 38;  m012 <- 90; y01 <- 15; N01 <- 1500; 
m021 <- 41; m022 <- 200; y02 <-  9; N02 <- 2500;
data <- c(z11, z12, z21, z22, m011, m012, m021, m022, y01, y02)

waldCI(data, N1, N2, N01, N02) 
margMLECI(data, N1, N2, N01, N02)
profMLECI(data, N1, N2, N01, N02)
approxMargMLECI(data, N1, N2, N01, N02)



## End(Not run)